Positive Solutions Of Some Nonlinear Elliptic Equations

In this thesis,we consider the existence and uniqueness of positive solutions of the nonlinear elliptic equations.First,we investigate the existence of positive solutions of the following semi-linear elliptic equations△u+f(x,u)+g(|x|)x·▽u=0,x∈ΩA and△u+f(x,u,▽u)=0,x∈ΩA, whereΩA={x∈Rn,|xl>A,n≥3).Second,we consider the followng equation div(|▽u|p2▽u)+f(x,u)+g(|x|)x·▽u=0,x∈ΩA. We present a sufficient condition of the existence of nonnegative solutions for 2>p>1,n≥p and n>p>2 respectively.Third,the existence of positive weak solutions is considered to the equation△u+g(|x|)x·▽u+a(x)uq-1=0, x∈Ω, u=0, x∈(?)Ω whereΩ(?)Rn\{0}is a bounded domain.Finally, a sufficient condition is given to guarantee the uniqueness of positive radial solutions of the semilinear elliptic equation△u+f(|x|,u)+g(|x|)x·▽u=0,x∈Ω, u=0, x∈(?)ΩwhereΩ={x∈Rn(n≥3),a<|x|<b).